{"ID":2897772,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.05535","arxiv_id":"2507.05535","title":"Special-Unitary Parameterization for Trainable Variational Quantum Circuits","abstract":"We propose SUN-VQC, a variational-circuit architecture whose elementary layers are single exponentials of a symmetry-restricted Lie subgroup, $\\mathrm{SU}(2^{k}) \\subset \\mathrm{SU}(2^{n})$ with $k \\ll n$. Confining the evolution to this compact subspace reduces the dynamical Lie-algebra dimension from $\\mathcal{O}(4^{n})$ to $\\mathcal{O}(4^{k})$, ensuring only polynomial suppression of gradient variance and circumventing barren plateaus that plague hardware-efficient ansätze. Exact, hardware-compatible gradients are obtained using a generalized parameter-shift rule, avoiding ancillary qubits and finite-difference bias. Numerical experiments on quantum auto-encoding and classification show that SUN-VQCs sustain order-of-magnitude larger gradient signals, converge 2--3$\\times$ faster, and reach higher final fidelities than depth-matched Pauli-rotation or hardware-efficient circuits. These results demonstrate that Lie-subalgebra engineering provides a principled, scalable route to barren-plateau-resilient VQAs compatible with near-term quantum processors.","short_abstract":"We propose SUN-VQC, a variational-circuit architecture whose elementary layers are single exponentials of a symmetry-restricted Lie subgroup, $\\mathrm{SU}(2^{k}) \\subset \\mathrm{SU}(2^{n})$ with $k \\ll n$. Confining the evolution to this compact subspace reduces the dynamical Lie-algebra dimension from $\\mathcal{O}(4^{...","url_abs":"https://arxiv.org/abs/2507.05535","url_pdf":"https://arxiv.org/pdf/2507.05535v1","authors":"[\"Kuan-Cheng Chen\",\"Huan-Hsin Tseng\",\"Samuel Yen-Chi Chen\",\"Chen-Yu Liu\",\"Kin K. Leung\"]","published":"2025-07-07T23:21:02Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"cs.LG\"]","methods":"[]","has_code":false}